Richard Burt, United States assistant secretary of state designate, stressed Dec. 9 that new NATO nuclear deployments planned for 1983-87 will proceed as scheduled unless there is prior Soviet-US arms agreement.

Negotiations could then continue after the initial deployment said Burt, in his capacity as chairman of the NATO special consultative group that monitors nuclear arms control. He also gave a new public figure, 333, for the number of Soviet mobile three-warhead SS-20s already deployed - the new Soviet weapon that future NATO Pershing II and cruise missiles are intended to counter. Under the two-thirds rule of thumb (one-third targeted on China, two-thirds on the West) this would mean about 222 of these missiles, with 666 warheads able to hit West Europe.

Burt's main aim seemed to be to scotch speculation (fueled by comments earlier this month by NATO Secretary-General Joseph Luns and British Defense Minister John Nott) about any shift at this point in the American ''zero-zero'' arms control proposal. Under this proposal NATO would not deploy its planned nuclear missiles only if the Soviet Union dismantles its already deployed SS-20 s.

NATO concern about slippage in the deployment has been nudged this month by Norway's near vote and Denmark's actual vote against future national contributions to the common infrastructure fund to pay for installation of the new missiles inside NATO countries. If this mood spreads to other NATO members, officials fear, pressure on Moscow to negotiate seriously would weaken; the USSR might think it could prevent the NATO deployments by fueling domestic European opposition to the missiles rather than making real arms control compromises of its own.

The Danish government has been at pains at the NATO meetings to stress its continued support for the missile deployments, according to various national spokesmen - and to emphasize that the Danish Folketing (Parliament) vote does not block the already committed Danish contributions in 1983.

The vote is an irritating reminder to NATO, however, of key parliamentary oposition to the new missiles in the Scandinavian and Benelux countries. It is doubtful whether the Dutch government, which initially agreed to take 48 cruise missiles later on, would ever get approval from the Parliament for deployment.

A similar though less urgent question arises with the other Benelux country committed to host cruise missiles, Belgium.

NATO's tack at the moment is to downplay this concern, however, especially since the governments of the three countries that will initiate the missile deployments at the end of next year - Britain, Italy, and West Germany - are firmly committed to proceeding with the stationing on time.

The new West German government has made clear from the beginning that it would proceed with the deployments in the absence of any arms control agreement.

Significantly, too, the West German Social Democrats in their new role in the opposition have not turned against the missiles, contrary to the earlier expectations of some observers. NATO is pursuing a similar tactic of deemphasizing Spain's reservations about its new NATO membership among the Spanish Socialists. The Spanish foreign minister is participating in the NATO foreign ministers' session - Spain's second after the previous conservative government joined NATO last summer. Spain is to abstain from signing the Dec. 10 NATO communique, however, and the Socialists campaign platform called for a referendum on NATO membership. NATO hopes that the experience of government responsibility will eventually move the Socialists toward ratifying NATO membership.